Abstract
A method for the evaluation of time-resolved entropy production in isothermal and incompressible flow is presented. It is applied as a postprocessing of the three-dimensional (3D) flow field obtained by time-resolved computational fluid dynamics (CFD) with scale adaptive turbulence modeling. Wall functions for direct and turbulent entropy production are presented for a cell-centered finite volume method, implemented in the open-source software OpenFOAM and validated on channel, asymmetric diffuser, and periodic hill flow. Single- and two-blade centrifugal pump flow is considered for a wide range of load conditions. Results are compared to experimental data. Time-averaged analysis shows essentially the same loss density distribution among pump components for both pumps, with the impeller and volute region contributing the most, especially in off-design conditions. For both pumps, the losses exhibit significant fluctuations due to impeller–volute interactions. The fluctuation magnitude of loss density is in the same range as flowrate fluctuations and much smaller than pressure fluctuation magnitude. For the two-blade pump (2BP), loss fluctuation magnitude is smaller than for the single-blade pump (1BP). Distinct loss mechanisms are identified for different load conditions. Upon blade passage, a promoted or attenuated volute tongue separation is imposed at part or overload, respectively. In between blade passages, a direct connection from pump inlet to the discharge leads to enhanced flowrate and loss density fluctuations. Future work aims at extending this analysis to stronger off-design conditions in multiblade pumps, where stochastic cycle fluctuations occur.
References
1.
Herwig
,
H.
, and
Kock
,
F.
, 2006
, “
Direct and Indirect Methods of Calculating Entropy Generation Rates in Turbulent Convective Heat Transfer Problems
,” Heat Mass Transfer
,
43
(3
), pp. 207
–215
.10.1007/s00231-006-0086-x2.
Bejan
,
A.
, 1979
, “
A Study of Entropy Generation in Fundamental Convective Heat Transfer
,” ASME J. Heat Mass Transfer-Trans. ASME
,
101
(4
), pp. 718
–725
.10.1115/1.34510633.
Bejan
,
A.
, 1980
, “
Second Law Analysis in Heat Transfer
,” Energy
,
5
(8–9
), pp. 720
–732
.10.1016/0360-5442(80)90091-24.
Bejan
,
A.
, and
Kestin
,
J.
, 1983
, “
Entropy Generation Through Heat and Fluid Flow
,” ASME J. Appl. Mech.
,
50
(2
), pp. 475
–475
.10.1115/1.31670725.
Kock
,
F.
, and
Herwig
,
H.
, 2004
, “
Local Entropy Production in Turbulent Shear Flows: A High-Reynolds Number Model With Wall Functions
,” Int. J. Heat Mass Transfer
,
47
(10–11
), pp. 2205
–2215
.10.1016/j.ijheatmasstransfer.2003.11.0256.
Kock
,
F.
, and
Herwig
,
H.
, 2005
, “
Entropy Production Calculation for Turbulent Shear Flows and Their Implementation in CFD Codes
,” Int. J. Heat Fluid Flow
,
26
(4
), pp. 672
–680
.10.1016/j.ijheatfluidflow.2005.03.0057.
Böhle
,
M.
,
Fleder
,
A.
, and
Mohr
,
M.
, 2016
, “
Study of the Losses in Fluid Machinery With the Help of Entropy
,” 16th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery
, Honolulu, HI, Apr. 10–15, pp. 1–9.https://hal.science/hal-018793718.
Pei
,
J.
,
Meng
,
F.
,
Li
,
Y.
,
Yuan
,
S.
, and
Chen
,
J.
, 2016
, “
Effects of Distance Between Impeller and Guide Vane on Losses in a Low Head Pump by Entropy Production Analysis
,” Adv. Mech. Eng.
,
8
(11
).10.1177/16878140166795689.
Li
,
X.
,
Zhu
,
Z.
,
Li
,
Y.
, and
Chen
,
X.
, 2016
, “
Experimental and Numerical Investigations of Head-Flow Curve Instability of a Single-Stage Centrifugal Pump With Volute Casing
,” Proc. Inst. Mech. Eng., Part A
,
230
(7
), pp. 633
–647
.10.1177/095765091666332610.
Li
,
D.
,
Gong
,
R.
,
Wang
,
H.
,
Xiang
,
G.
,
Wei
,
X.
, and
Qin
,
D.
, 2016
, “
Entropy Production Analysis for Hump Characteristics of a Pump Turbine Model
,” Chin. J. Mech. Eng.
,
29
(4
), pp. 803
–812
.10.3901/CJME.2016.0414.05211.
Cao
,
J.
,
Pei
,
J.
,
Gu
,
Y.
,
Wang
,
W.
, and
Yuan
,
S.
, 2019
, “
Flow Losses Analysis in a Mixed Flow Pump With Annular Volute by Entropy Production Evaluation
,” IOP Conf. Ser.: Earth Environ. Sci.
,
240
, p. 032047
.10.1088/1755-1315/240/3/03204712.
Koranteng Osman
,
M.
,
Wang
,
W.
,
Yuan
,
J.
,
Zhao
,
J.
,
Wang
,
Y.
, and
Liu
,
J.
, 2019
, “
Flow Loss Analysis of a Two-Stage Axially Split Centrifugal Pump With Double Inlet Under Different Channel Designs
,” Proc. Inst. Mech. Eng., Part C
,
233
(15
), pp. 5316
–5328
.10.1177/095440621984357313.
Zhao
,
X.
,
Luo
,
Y.
,
Wang
,
Z.
,
Xiao
,
Y.
, and
Avellan
,
F.
, 2019
, “
Unsteady Flow Numerical Simulations on Internal Energy Dissipation for a Low-Head Centrifugal Pump at Part-Load Operating Conditions
,” Energies
,
12
(10
), p. 2013
.10.3390/en1210201314.
Melzer
,
S.
,
Pesch
,
A.
,
Schepeler
,
S.
,
Kalkkuhl
,
T.
, and
Skoda
,
R.
, 2020
, “
Three-Dimensional Simulation of Highly Unsteady and Isothermal Flow in Centrifugal Pumps for the Local Loss Analysis Including a Wall Function for Entropy Production
,” ASME J. Fluids Eng.
,
142
(11
), p. 111209
.10.1115/1.404796715.
Melzer
,
S.
, 2021
, “
Experimental Investigations and 3D Flow Simulations of a Single-Blade and a Two-Blade Pump for the Analysis of Unsteady Characteristics and Local Losses
,” Dissertation
,
Ruhr-Universität Bochum
,
Bochum, Germany
.https://www.shaker.de/Online-Gesamtkatalog-Download/2024.03.25-13.35.47-180.94.14.2-radC6CD2.tmp/3-8440-8166-6_INH.PDF16.
Casimir
,
N.
,
Zhu
,
X.
,
Hundshagen
,
M.
,
Ludwig
,
G.
, and
Skoda
,
R.
, 2020
, “
Numerical Study of Rotor-Stator Interaction of a Centrifugal Pump at Part Load With Special Emphasis on Unsteady Blade Load
,” ASME J. Fluids Eng.
,
142
(8
) p. 081203
.10.1115/1.404662217.
Hundshagen
,
M.
,
Casimir
,
N.
,
Pesch
,
A.
,
Falsafi
,
S.
, and
Skoda
,
R.
, 2020
, “
Assessment of Scale-Adaptive Turbulence Models for Volute-Type Centrifugal Pumps at Part Load Operation
,” Int. J. Heat Fluid Flow
,
85
, p. 108621
.10.1016/j.ijheatfluidflow.2020.10862118.
Zamiri
,
A.
, and
Chung
,
J. T.
, 2018
, “
Numerical Evaluation of Turbulent Flow Structures in a Stirred Tank With a Rushton Turbine Based on Scale-Adaptive Simulation
,” Comput. Fluids
,
170
, pp. 236
–248
.10.1016/j.compfluid.2018.05.00719.
Rave
,
K.
,
Lehmenkühler
,
M.
,
Wirz
,
D.
,
Bart
,
H.-J.
, and
Skoda
,
R.
, 2021
, “
3D Flow Simulation of a Baffled Stirred Tank for an Assessment of Geometry Simplifications and a Scale-Adaptive Turbulence Model
,” Chem. Eng. Sci.
,
231
, p. 116262
.10.1016/j.ces.2020.11626220.
Thamsen
,
P. U.
,
Bubelach
,
T.
,
Pensler
,
T.
, and
Springer
,
P.
, 2008
, “
Cavitation in Single-Vane Sewage Pumps
,” Int. J. Rotating Mach.
,
2008
, pp. 1
–6
.10.1155/2008/35402021.
Thamsen
,
P. U.
,
Lee
,
A.
, and
Oesterle
,
M.
, 2008
, “
Reliability Improvements in Sewage Pumping Using Diagnosis With Active Reaction
,” Water Pract. Technol.
,
3
(4
), pp. 1
–8
.10.2166/wpt.2008.08822.
Aoki
,
M.
, 1984
, “
Instantaneous Interblade Pressure Distributions and Fluctuating Radial Thrust in a Single-Blade Centrifugal Pump
,” Bull. JSME
,
27
(233
), pp. 2413
–2420
.10.1299/jsme1958.27.241323.
Benra
,
F. K.
,
Dohmen
,
H. J.
, and
Sommer
,
M.
, 2006
, “
Flow Field Visualization of a Single-Blade Centrifugal Pump Using PIV-Method — Comparison to Numerical Results
,” J. Visualization
,
9
(4
), pp. 358
–358
.10.1007/BF0318177124.
Daly
,
J.
,
de Souza
,
B.
,
Niven
,
A.
, and
Frawley
,
P.
, 2006
, “
Numerical Simulation of Transient Flow and Head Distribution Through a Single Blade Centrifugal Pump Impeller
,” Proceedings of the 4th WSEAS International Conference on Fluid Mechanics and Aerodynamics
, Elounda, Greece, Aug. 21–23, pp. 349
–354
.25.
Okamura
,
T.
, 1980
, “
Radial Thrust in Centrifugal Pumps With a Single-Vane Impellers
,” Bull. JSME
,
23
(180
), pp. 895
–901
.10.1299/jsme1958.23.89526.
Savilius
,
N.
, and
Benra
,
F.-K.
, 2006
, “
Experimental Investigation of Transient Hydrodynamic Forces of a Single-Blade Centrifugal Pump
,” Proceedings of the 4th WSEAS International Conference on Fluid Mechanics and Aerodynamics
, Elounda, Greece, Aug. 21–23, pp. 331
–336
.http://www.wseas.us/e-library/conferences/2006elounda2/papers/538-195.pdf27.
Zwingenberg
,
M.
, and
Benra
,
F. K.
, 2006
, “
Measurement of the Periodic Unsteady Flow in a Single-Blade Centrifugal Pump by PIV-Method
,” Proceedings of the 4th WSEAS International Conference on Fluid Mechanics and Aerodynamics
, Elounda, Greece, Aug. 21–23, pp. 325
–330
.28.
Melzer
,
S.
,
Müller
,
T.
,
Schepeler
,
S.
,
Kalkkuhl
,
T.
, and
Skoda
,
R.
, 2019
, “
Experimental and Numerical Investigation of the Transient Characteristics and Volute Casing Wall Pressure Fluctuations of a Single-Blade Pump
,” Proc. Inst. Mech. Eng., Part E
,
233
(2
), pp. 280
–291
.10.1177/095440891878052429.
Melzer
,
S.
,
Munsch
,
P.
,
Förster
,
J.
,
Friderich
,
J.
, and
Skoda
,
R.
, 2020
, “
A System for Time-Fluctuating Flow Rate Measurements in a Single-Blade Pump Circuit
,” Flow Meas. Instrum.
,
71
, p. 101675
.10.1016/j.flowmeasinst.2019.10167530.
Pesch
,
A.
,
Melzer
,
S.
,
Schepeler
,
S.
,
Kalkkuhl
,
T.
, and
Skoda
,
R.
, 2021
, “
Pressure and Flow Rate Fluctuations in Single- and Two-Blade Pumps
,” ASME J. Fluids Eng.
,
143
(1
), p. 011203
.10.1115/1.404814231.
Casimir
,
N.
,
Xiangyuan
,
Z.
,
Ludwig
,
G.
, and
Skoda
,
R.
, 2019
, “
Assessment of Statistical Eddy-Viscosity Turbulence Models for Unsteady Flow at Part and Overload Operation of Centrifugal Pumps
,” Proceedings of 13th European Conference on Turbomachinery Fluid Dynamics and Thermodynamics (ETC'13
), Lausanne, Switzerland, Apr. 8–12, pp. 1–13.10.29008/ETC2019-04732.
Konnigk
,
L.
,
Torner
,
B.
,
Bruschewski
,
M.
,
Grundmann
,
S.
, and
Wurm
,
F.-H.
, 2021
, “
Equivalent Scalar Stress Formulation Taking Into Account Non-Resolved Turbulent Scales
,” Cardiovasc. Eng. Technol.
,
12
(3
), pp. 251
–272
.10.1007/s13239-021-00526-x33.
Torner
,
B.
,
Konnigk
,
L.
,
Abroug
,
N.
, and
Wurm
,
H.
, 2021
, “
Turbulence and Turbulent Flow Structures in a Ventricular Assist device-A Numerical Study Using the Large-Eddy Simulation
,” Int. J. Numer. Methods Biomed. Eng.
,
37
(3
), p. e3431
.10.1002/cnm.343134.
Sorguven
,
E.
,
Incir
,
S.
, and
Highgate
,
J.
, 2022
, “
Understanding Loss Generation Mechanisms in a Centrifugal Pump Using Large Eddy Simulation
,” Int. J. Heat Fluid Flow
,
96
, p. 108994
.10.1016/j.ijheatfluidflow.2022.10899435.
Ries
,
F.
,
Li
,
Y.
,
Klingenberg
,
D.
,
Nishad
,
K.
,
Janicka
,
J.
, and
Sadiki
,
A.
, 2018
, “
Near-Wall Thermal Processes in an Inclined Impinging Jet: Analysis of Heat Transport and Entropy Generation Mechanisms
,” Energies
,
11
(6
), p. 1354
.10.3390/en1106135436.
Ries
,
F.
,
Li
,
Y.
,
Nishad
,
K.
,
Janicka
,
J.
, and
Sadiki
,
A.
, 2019
, “
Entropy Generation Analysis and Thermodynamic Optimization of Jet Impingement Cooling Using Large Eddy Simulation
,” Entropy
,
21
(2
), p. 129
.10.3390/e2102012937.
Ries
,
F.
, 2019
, Numerical Modeling and Prediction of Irreversibilities in Sub- and Supercritical Turbulent Near-Wall Flows
,
Universitäts- und Landesbibliothek Darmstadt
,
Darmstadt, Germany
.38.
Safari
,
M.
,
Sheikhi
,
M. R. H.
,
Janbozorgi
,
M.
, and
Metghalchi
,
H.
, 2010
, “
Entropy Transport Equation in Large Eddy Simulation for Exergy Analysis of Turbulent Combustion Systems
,” Entropy
,
12
(3
), pp. 434
–444
.10.3390/e1203043439.
Safari
,
M.
,
Hadi
,
F.
, and
Sheikhi
,
M.
, 2014
, “
Progress in the Prediction of Entropy Generation in Turbulent Reacting Flows Using Large Eddy Simulation
,” Entropy
,
16
(10
), pp. 5159
–5177
.10.3390/e1610515940.
Fröhlich
,
J.
, 2006
, Large Eddy Simulation Turbulenter Strömungen
, 1st ed.,
Teubner
, Wiesbaden, Germany
.41.
42.
Posa
,
A.
,
Lippolis
,
A.
,
Verzicco
,
R.
, and
Balaras
,
E.
, 2011
, “
Large-Eddy Simulations in Mixed-Flow Pumps Using an Immersed-Boundary Method
,” Comput. Fluids
,
47
(1
), pp. 33
–43
.10.1016/j.compfluid.2011.02.00443.
Posa
,
A.
,
Lippolis
,
A.
, and
Balaras
,
E.
, 2015
, “
Large-Eddy Simulation of a Mixed-Flow Pump at Off-Design Conditions
,” ASME J. Fluids Eng.
,
137
(10
), p. 101302
.10.1115/1.403048944.
Kim
,
J.-H.
, and
Choi
,
Y.-S.
, 2018
, “
State-of-the-Art Design Technique of a Single-Channel Pump for Wastewater Treatment
,” Wastewater and Water Quality
,
T.
Yonar
, ed.,
InTech
, Rijeka, Croatia
.45.
Kye
,
B.
,
Park
,
K.
,
Choi
,
H.
,
Lee
,
M.
, and
Kim
,
J.-H.
, 2018
, “
Flow Characteristics in a Volute-Type Centrifugal Pump Using Large Eddy Simulation
,” Int. J. Heat Fluid Flow
,
72
, pp. 52
–60
.10.1016/j.ijheatfluidflow.2018.04.01646.
Pacot
,
O.
,
Kato
,
C.
,
Guo
,
Y.
,
Yamade
,
Y.
, and
Avellan
,
F.
, 2016
, “
Large Eddy Simulation of the Rotating Stall in a Pump-Turbine Operated in Pumping Mode at a Part-Load Condition
,” ASME J. Fluids Eng.
,
138
(11
), p. 111102
.10.1115/1.403342347.
Spalart
,
P. R.
, 2009
, “
Detached-Eddy Simulation
,” Annu. Rev. Fluid Mech.
,
41
(1
), pp. 181
–202
.10.1146/annurev.fluid.010908.16513048.
Menter
,
F.
,
Kuntz
,
M.
, and
Bender
,
R.
, 2003
, “
A Scale-Adaptive Simulation Model for Turbulent Flow Predictions
,” 41st Aerospace Sciences Meeting and Exhibit
, Reno, NV, Jan. 6–9, p. 767
.10.2514/6.2003-76749.
Gritskevich
,
M. S.
,
Garbaruk
,
A. V.
,
Schütze
,
J.
, and
Menter
,
F. R.
, 2012
, “
Development of DDES and IDDES Formulations for the k-ω Shear Stress Transport Model
,” Flow, Turbul. Combust.
,
88
(3
), pp. 431
–449
.10.1007/s10494-011-9378-450.
Menter
,
F.
, 2018
, “
Stress-Blended Eddy Simulation (SBES)—A New Paradigm in Hybrid RANS-LES Modeling
,” Progress in Hybrid RANS-LES Modelling
(Notes on Numerical Fluid Mechanics and Multidisciplinary Design), Vol.
137
,
Y.
Hoarau
,
S.-H.
Peng
,
D.
Schwamborn
, and
A.
Revell
eds.,
Springer International Publishing
,
Cham
, pp. 27
–37
.51.
Menter
,
F.
,
Hüppe
,
A.
,
Matyushenko
,
A.
, and
Kolmogorov
,
D.
, 2021
, “
An Overview of Hybrid RANS–LES Models Developed for Industrial CFD
,” Appl. Sci.
,
11
(6
), p. 2459
.10.3390/app1106245952.
Cui
,
B.
,
Zhang
,
C.
,
Zhang
,
Y.
, and
Zhu
,
Z.
, 2020
, “
Influence of Cutting Angle of Blade Trailing Edge on Unsteady Flow in a Centrifugal Pump Under Off-Design Conditions
,” Appl. Sci.
,
10
(2
), p. 580
.10.3390/app1002058053.
Zhang
,
N.
,
Liu
,
X.
,
Gao
,
B.
,
Wang
,
X.
, and
Xia
,
B.
, 2019
, “
Effects of Modifying the Blade Trailing Edge Profile on Unsteady Pressure Pulsations and Flow Structures in a Centrifugal Pump
,” Int. J. Heat Fluid Flow
,
75
, pp. 227
–238
.10.1016/j.ijheatfluidflow.2019.01.00954.
Zhang
,
T.
,
Wu
,
D.
,
Qiu
,
S.
,
Zhou
,
P.
,
Ren
,
Y.
, and
Mou
,
J.
, 2022
, “
LES Analysis of the Unsteady Flow Characteristics of a Centrifugal Pump Impeller
,” Fluid Dyn. Mater. Process.
,
18
(5
), pp. 1349
–1361
.10.32604/fdmp.2022.01961755.
Zhou
,
P.
,
Dai
,
J.
,
Yan
,
C.
,
Zheng
,
S.
,
Ye
,
C.
, and
Zhang
,
X.
, 2019
, “
Effect of Stall Cells on Pressure Fluctuations Characteristics in a Centrifugal Pump
,” Symmetry
,
11
(9
), p. 1116
.10.3390/sym1109111656.
Xin
,
T.
,
Zhili
,
L.
,
Meng
,
Z.
,
Haotian
,
Y.
,
Wei
,
J.
,
Yuchuan
,
W.
, and
Diyi
,
C.
, 2021
, “
Analysis of Unsteady Flow Characteristics of Centrifugal Pump Under Part Load Based on DDES Turbulence Model
,” Shock Vib.
,
2021
, pp. 1
–11
.10.1155/2021/997080057.
Zhang
,
N.
,
Liu
,
X.
,
Gao
,
B.
, and
Xia
,
B.
, 2019
, “
DDES Analysis of the Unsteady Wake Flow and Its Evolution of a Centrifugal Pump
,” Renewable Energy
,
141
, pp. 570
–582
.10.1016/j.renene.2019.04.02358.
Torner
,
B.
,
Konnigk
,
L.
, and
Wurm
,
F.-H.
, 2019
, “
Influence of Turbulent Shear Stresses on the Numerical Blood Damage Prediction in a Ventricular Assist Device
,” Int. J. Artif. Organs
,
42
(12
), pp. 735
–747
.10.1177/039139881986139559.
Torner
,
B.
,
Konnigk
,
L.
,
Hahne
,
M.
, and
Wurm
,
F.-H.
, 2021
, “
Computation of Dissipation Rates in Turbo Pumps Using Different Simulation Methods
,” 14th European Conference on Turbomachinery Fluid Dynamics and Thermodynamics, European Turbomachinery Society
, Gdansk, Poland, Apr 12–16, pp. 1
–15
.https://www.euroturbo.eu/paper/ETC2021-689.pdf60.
Egorov
,
Y.
, and
Menter
,
F.
, 2008
, “
Development and Application of SST-SAS Turbulence Model in the DESIDER Project
,” Advances in Hybrid RANS-LES Modelling
,
Springer
,
Berlin, Heidelberg
, pp. 261
–270
.61.
Jakirlić
,
S.
,
Bopp
,
M.
,
Chang
,
C.-Y.
,
Köhler
,
F.
,
Krumbein
,
B.
,
Kutej
,
L.
,
Kütemeier
,
D.
, et al., 2019
, “
RANS-Based Sub-Scale Modelling in Eddy-Resolving Simulation Methods
,” ERCOFTAC Bull.
,
121
, pp. 5
–16
.https://www.ercoftac.org/publications/ercoftac_bulletin/bulletin-122/62.
Lucius
,
A.
, and
Brenner
,
G.
, 2010
, “
Unsteady CFD Simulations of a Pump in Part Load Conditions Using Scale-Adaptive Simulation
,” Int. J. Heat Fluid Flow
,
31
(6
), pp. 1113
–1118
.10.1016/j.ijheatfluidflow.2010.06.00563.
Pavesi
,
G.
,
Dazin
,
A.
,
Cavazzini
,
G.
,
Caignaert
,
G.
,
Bois
,
G.
, and
Ardizzon
,
G.
, 2011
, “
Experimental and Numerical Investigation of Unforced Unsteadiness in a Vaneless Radial Diffuser
,” 9th European Conference on Turbomachinery: Fluid Dynamics and Thermodynamics, ETC 2011 - Conference Proceedings
, Istanbul, Turkey, Mar. 21–25, pp. 625
–636
.https://hal.science/hal-0079434264.
Schiffer-Rosenberger
,
J.
,
Bodner
,
C.
, and
Jaberg
,
H.
, 2016
, “
Performance Analysis of a Single-Blade Impeller Pump Based on Unsteady 3D Numerical Simulation
,” Proceedings of the 3rd International Rotating Equipment Conference
, Düsseldorf, Germany, Sept. 14–15, pp. 193
–203
.https://www.researchgate.net/publication/312032849_Performance_analysis_of_a_single-blade_impeller_pump_based_on_unsteady_3D_numerical_simulation65.
Si
,
Q.
,
Yuan
,
J.
,
Yuan
,
S.
,
Wang
,
W.
,
Zhu
,
L.
, and
Bois
,
G.
, 2014
, “
Numerical Investigation of Pressure Fluctuation in Centrifugal Pump Volute Based on SAS Model and Experimental Validation
,” Adv. Mech. Eng.
,
6
, p. 972081
.10.1155/2014/97208166.
Witte
,
M.
,
Kranz
,
O.
,
Torner
,
B.
, and
Wurm
,
F. H.
, 2019
, “
Investigation of the Wall Pressure Fluctuations, the Operational Deflection Shapes and the Airborne Noise Radiation of a Single Stage Radial Pump
,” 13th European Conference on Turbomachinery Fluid Dynamics and Thermodynamics, European Turbomachinery Society
, Lausanne, Switzerland, Apr 8–12, pp. 1
–13
.https://www.euroturbo.eu/paper/ETC2019-071.pdf67.
Zhang
,
W.
,
Yu
,
Y.
, and
Chen
,
H.
, 2010
, “
Numerical Simulation of Unsteady Flow in Centrifugal Pump Impeller at Off-Design Condition by Hybrid RANS/LES Approaches
,” High Performance Computing and Applications
(Lecture Notes in Computer Science), Vol.
5938
,
Springer
,
Berlin Heidelberg
, pp. 571
–578
.68.
Fröhlich
,
J.
, and
von Terzi
,
D.
, 2008
, “
Hybrid LES/RANS Methods for the Simulation of Turbulent Flows
,” Prog. Aerosp. Sci.
,
44
(5
), pp. 349
–377
.10.1016/j.paerosci.2008.05.00169.
Menter
,
F. R.
, and
Egorov
,
Y.
, 2010
, “
The Scale-Adaptive Simulation Method for Unsteady Turbulent Flow Predictions. Part 1: Theory and Model Description
,” Flow, Turbul. Combust.
,
85
(1
), pp. 113
–138
.10.1007/s10494-010-9264-570.
Menter
,
F.
, 1994
, “
Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications
,” AIAA J.
,
32
(8
), pp. 1598
–1605
.10.2514/3.1214971.
Menter
,
F.
,
Kuntz
,
M.
, and
Langtry
,
R. B.
, 2003
, “
Ten Years of Industrial Experience With the SST Turbulence Model
,” Heat Mass Transfer
,
4
(1
), pp. 1
–8
.https://www.researchgate.net/publication/228742295_Ten_years_of_industrial_experience_with_the_SST_turbulence_model72.
Kalitzin
,
G.
,
Medic
,
G.
,
Iaccarino
,
G.
, and
Durbin
,
P.
, 2005
, “
Near-Wall Behavior of RANS Turbulence Models and Implications for Wall Functions
,” J. Comput. Phys.
,
204
(1
), pp. 265
–291
.10.1016/j.jcp.2004.10.01873.
Menter
,
F.
, and
Esch
,
T.
, 2001
, “
Elements of Industrial Heat Transfer Prediction
,” 16th Brazilian Congress of Mechanical Engineering
, Brazilian Society of Mechanical Sciences, Uberlândia, Minas Gerais, Brazil, pp. 117
–127
.74.
Vieser
,
W.
,
Esch
,
T.
, and
Menter
,
F. R.
, 2002
, “
Heat Transfer Predictions Using Advanced Two-Equation Turbulence Models
,” CFX Technical Memorandum, CFX Technical Memorandum.75.
Nicoud
,
F.
, and
Ducros
,
F.
, 1999
, “
Subgrid-Scale Stress Modelling Based on the Square of the Velocity Gradient Tensor
,” Flow, Turbul. Combust.
,
62
(3
), pp. 183
–200
.10.1023/A:100999542600176.
Kock
,
F.
,
Herwig
,
H.
, and
Kabelac
,
S.
, 2003
, Bestimmung Der Lokalen Entropieproduktion in Turbulenten Strömungen Und Deren Nutzung Zur Bewertung Konvektiver Transportprozesse
,
Berichte Aus Der Strömungstechnik
,
Shaker, Aachen
.77.
Rave
,
K.
,
Hermes
,
M.
,
Hundshagen
,
M.
, and
Skoda
,
R.
, 2023
, “
Assessment of Scale-Adaptive Turbulence Modeling in Coupled CFD-PBM 3D Flow Simulations of Disperse Liquid-Liquid Flow in a Baffled Stirred Tank With Particular Emphasis on the Dissipation Rate
,” Chem. Eng. Sci.
,
270
, p. 118509
.10.1016/j.ces.2023.11850978.
Lilly
,
D.
, 1966
, “
The Representation of Small-Scale Turbulence in Numerical Simulation Experiments
,” Pre-publication Review Copy, National Center for Atmospheric Research, NCAR Library (NCARLIB).79.
ANSYS
, 2017
, “
ANSYS ICEM CFD Help Manual
,” ANSYS Inc., Canonsburg, PA.80.
Issa
,
R. I.
, 1986
, “
Solution of the Implicitly Discretised Fluid Flow Equations by Operator-Splitting
,” J. Comput. Phys.
,
62
(1
), pp. 40
–65
.10.1016/0021-9991(86)90099-981.
Patankar
,
S. V.
, and
Spalding
,
D. B.
, 1983
, “
A Calculation Procedure for Heat, Mass and Momentum Transfer in Three-Dimensional Parabolic Flows
,” Numerical Prediction of Flow, Heat Transfer, Turbulence and Combustion
,
Elsevier
, Amsterdam, The Netherlands
, pp. 54
–73
.10.1016/B978-0-08-030937-8.50013-182.
Hundshagen
,
M.
,
Mansour
,
M.
,
Thévenin
,
D.
, and
Skoda
,
R.
, 2021
, “
3D Simulation of Gas-Laden Liquid Flows in Centrifugal Pumps and the Assessment of Two-Fluid CFD Methods
,” Exp. Comput. Multiphase Flow
,
3
(3
), pp. 186
–207
.10.1007/s42757-020-0080-483.
Strelets
,
M.
, 2001
, “
Detached Eddy Simulation of Massively Separated Flows
,” 39th Aerospace Sciences Meeting
, American Institute of Aeronautics and Astronautics, Reno, NV, Jan. 8–11, pp. 1
–18
.10.2514/6.2001-87984.
Travin
,
A.
,
Shur
,
M.
,
Strelets
,
M.
, and
Spalart
,
P. R.
, 2002
, “
Physical and Numerical Upgrades in the Detached-Eddy Simulation of Complex Turbulent Flows
,” Advances in LES of Complex Flows
(Fluid Mechanics and Its Applications), Vol.
65
,
R.
Moreau
,
R.
Friedrich
, and
W.
Rodi
, eds.,
Springer
,
Dordrecht
, The Netherlands, pp. 239
–254
.85.
Warming
,
R. F.
, and
Beam
,
R. M.
, 1976
, “
Upwind Second-Order Difference Schemes and Applications in Aerodynamic Flows
,” AIAA J.
,
14
(9
), pp. 1241
–1249
.10.2514/3.6145786.
Weller
,
H.
, 2012
, “
Controlling the Computational Modes of the Arbitrarily Structured C Grid
,” Mon. Weather Rev.
,
140
(10
), pp. 3220
–3234
.10.1175/MWR-D-11-00221.187.
Martínez
,
J.
,
Piscaglia
,
F.
,
Montorfano
,
A.
,
Onorati
,
A.
, and
Aithal
,
S. M.
, 2015
, “
Influence of Spatial Discretization Schemes on Accuracy of Explicit LES: Canonical Problems to Engine-Like Geometries
,” Comput. Fluids
,
117
, pp. 62
–78
.10.1016/j.compfluid.2015.05.00788.
Cao
,
Y.
, and
Tamura
,
T.
, 2016
, “
Large-Eddy Simulations of Flow Past a Square Cylinder Using Structured and Unstructured Grids
,” Comput. Fluids
,
137
, pp. 36
–54
.10.1016/j.compfluid.2016.07.01389.
Davidson
,
L.
, 2006
, “
Evaluation of the SST-SAS Model: Channel Flow, Asymmetric Diffuser and Axi-Symmetric Hill
,” European Conference on Computational Fluid Dynamics ECCOMAS CFD
, Egmond aan Zee, The Netherlands, Sept. 5–9, pp. 1
–20
.https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=fc0f0d2e134244069383047f3abafb872e1b01b890.
Obi
,
S.
,
Ohimuzi
,
H.
,
Aoki
,
K.
, and
Masuda
,
S.
, 1993
, “
Experimental and Computational Study of Turbulent Separating Flow in an Asymmetric Plane Diffuser
,” 9th Symposium on Turbulent Shear Flows
,
Kyoto, Japan
, Aug. 16–18, pp. 1
–4
.https://www.researchgate.net/profile/Shinnosuke-Obi/publication/261851014_Experimental_and_Computational_Study_of_Turbulent_Separating_Flow_in_an_Asymmetric_Plane_Diffuser/links/5595f3d208ae99aa62c740f4/Experimental-and-Computational-Study-of-Turbulent-Separating-Flow-in-an-Asymmetric-Plane-Diffuser.pdf91.
Balakumar
,
P.
, and
Park
,
G. I.
, 2015
, “
DNS/LES Simulations of Separated Flows at High Reynolds Numbers
,” AIAA
Paper No. 2015-2783.10.2514/6.2015-278392.
Fröhlich
,
J.
,
Mellen
,
C. P.
,
Rodi
,
W.
,
Temmerman
,
L.
, and
Leschziner
,
M. A.
, 2005
, “
Highly Resolved Large-Eddy Simulation of Separated Flow in a Channel With Streamwise Periodic Constrictions
,” J. Fluid Mech.
,
526
, pp. 19
–66
.10.1017/S002211200400281293.
Vreman
,
B.
,
Geurts
,
B.
, and
Kuerten
,
H.
, 1994
, “
Discretization Error Dominance Over Subgrid Terms in Large Eddy Simulation of Compressible Shear Layers in 2D
,” Commun. Numer. Methods Eng.
,
10
(10
), pp. 785
–790
.10.1002/cnm.164010100494.
Ghosal
,
S.
, 1996
, “
An Analysis of Numerical Errors in Large-Eddy Simulations of Turbulence
,” J. Comput. Phys.
,
125
(1
), pp. 187
–206
.10.1006/jcph.1996.008895.
Kravchenko
,
A. G.
, and
Moin
,
P.
, 1997
, “
On the Effect of Numerical Errors in Large Eddy Simulations of Turbulent Flows
,” J. Comput. Phys.
,
131
(2
), pp. 310
–322
.10.1006/jcph.1996.559796.
Mohammadi
,
S.
, and
Skoda
,
R.
, 2018
, “
Assessment of Static and Dynamic Wall-Adapting Subgrid-Scale Models for Turbulent Channel and Square Duct Flows
,” Turbulence and Interactions
(Notes on Numerical Fluid Mechanics and Multidisciplinary Design), Vol.
135
,
Springer International Publishing
, pp. 185
–197
.97.
DIN9906
, 2012
, “
Rotodynamic Pumps–Hydraulic Performance Acceptance Tests
” International Organisation for Standardisation, Geneva, Switzerland, Beuth Verlag GmbH.98.
Munsch
,
P.
,
Lehr
,
C.
,
Brümmer
,
A.
, and
Skoda
,
R.
, 2023
, “
A Compressible, Coupled Three-Dimensional/One-Dimensional Flow Solution Method for the Seamless Simulation of Centrifugal Pumps and Their Piping
,” ASME J. Fluids Eng.
,
145
(9
), p. 091203
.10.1115/1.4062322
